This paper presents and solves the maximum throughput dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which the flow on each arc not only has an associated upper and lower bound but also an associated transit time. Flow is to be sent through the network in each period so as to satisfy...

We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bound...

In contrast to traditional flow networks, in additive flow networks, to every edge e is assigned a gain factor g(e) which represents the loss or gain of the flow while using edge e. Hence, if a flow f(e) enters the edge e and f(e) is less than the designated capacity of e, then f(e) + g(e) ≥ 0 units of flow reach the end point of e, provided e is used, i.e., provided f(e) ≠ 0. In this report we...

In this paper, a multi-perspective decision support system (MP-DSS)‎ ‎to design hierarchical public transportation network is developed‎. ‎Since this problem depends on different perspectives‎, ‎MP-DSS consists of two sub-systems with macro and micro sub-systems based on travel information‎, ‎land use and expert knowledge‎. ‎In the micro sub-system‎, ‎two sub-modules are developed considering o...

In the classical maximal flow problem, the objective is to maximize the supply to a single sink in a capacitated network. In this paper we consider general capacitated networks with multiple sinks: the objective is to optimize a general "concave" preference relation on the set of feasible supply vectors. We show that an optimal solution can be obtained by a marginal allocation procedure. An eff...

Two special and important network flow problems are the maximal flow problem and the shortest path problem. Both of these problems can be solved by either the network simplex method of Chapter 9 or the out-of-kilter algorithm of Chapter 11. However, their frequent occurrence in practice and the specialized, more efficient procedures that can be developed for handling these two problems provide ...

For the earliest arrival flow problem one is given a network G = (V,A) with capacities u(a) and transit times τ(a) on its arcs a ∈ A, together with a source and a sink vertex s, t ∈ V . The objective is to send flow from s to t that moves through the network over time, such that for each point in time θ ∈ [0, T ) the maximum possible amount of flow reaches t. If, for each θ ∈ [0, T ) this flow ...